2.10 Logarithmic scaling and linearizing dataIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

What does an increase of 1 on a \log{10} scale mean?
Why use a logarithmic scale?
Linearize y=ab^{x}.
Gradient and intercept for \ln y against x (exponential model)?
Linearize y=kx^{n}.
Gradient and intercept for \ln y against \ln x (power model)?
What is a semi-log graph?
What is a log-log graph?
Which law of logarithms turns \ln(x^n) into something linear?
What does Pearson's r close to \pm1 tell you after linearizing?
Do you need to draw log graphs in the exam?
Why be careful predicting beyond the data?

Exam questions on 2.10 Logarithmic scaling and linearizing data

A researcher studies samples in which the number of cells $N$ ranges from 20 to 3 000 000, so she records $\log_{10}N$ instead of $N$ .
A sample has $\log_{10}N=4.5$ . Find $N$ , correct to 3 significant figures.2 marks
The number of bacteria $N$ in a culture after $t$ hours is modelled by $N=ab^{t}$ , where $a$ and $b$ are constants. The relationship between $\ln N$ and $t$ is linear, with gradient $0.35$ and vertical intercept $4.2$ .
Find the value of $a$ and state what it represents.2 marks
The orbital period $T$ (days) of a planet and its mean distance $d$ (million km) from the Sun are modelled by $T=kd^{n}$ . Data for four planets, with $d$ from 57.9 to 228, give the line of best fit $\log_{10}T=1.5\log_{10}d-0.70$ .
By taking logarithms of $T=kd^{n}$ , find the values of $n$ and $k$ .3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).